An efficient workflow for modelling high-dimensional spatial extremes

Abstract

We develop a comprehensive methodological workflow for Bayesian modelling of high-dimensional spatial extremes that lets us describe both weakening extremal dependence at increasing levels and changes in the type of extremal dependence class as a function of the distance between locations. This is achieved with a latent Gaussian version of the spatial conditional extremes model that allows for computationally efficient inference with R-INLA. Inference is made more robust using a post hoc adjustment method that accounts for possible model misspecification. This added robustness makes it possible to extract more information from the available data during inference using a composite likelihood. The developed methodology is applied to the modelling of extreme hourly precipitation from high-resolution radar data in Norway. Inference is performed quickly, and the resulting model fit successfully captures the main trends in the extremal dependence structure of the data. The post hoc adjustment is found to further improve model performance.